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At least 1,747 records · Page 97

C++ Resource Intelligent Compilation for GPU Enabled Applications

We are nearing the limits of Moore's Law with current computing technology. As industries push for more performance from smaller systems, alternate methods of computation such as Graphics Processing Units (GPUs) should be considered. Many of these systems utilize the Compute Unified Device Architecture (CUDA) to give programmers access to individual compute elements of the GPU for general purpose computing tasks. Direct access to the GPU's parallel multi-core architecture enables highly efficient computation and can drastically reduce the time required for complex algorithms or data analysis. Of course not all systems have a CUDA-enabled device to leverage, and so applications must consider optional support for users with these devices. Resource Intelligent Compilation (RIC) addresses this situation by enabling GPU-based acceleration of existing applications without affecting users without GPUs. Resource Intelligent Compilation (RIC) creates C/C++ modules that can be compiled to create a standard CPU version or GPU accelerated version of a program, depending on hardware availability. This is accomplished through a toolbox of programming strategies based on features of the CUDA API. Using this toolbox, existing applications can be modified with ease to support GPU acceleration, and new applications can be generated with just a few simple modifications. All of this culminates in an accelerated application for users with the appropriate hardware, with no performance impact to standard systems. This memorandum presents all the important features involved in supporting and implementing RIC and an example of using RIC to accelerate an existing mathematical model, without removing support for standard users. Through this memorandum, NASA engineers can acquire a set of guidelines to follow for RIC-compliant development, seamlessly accelerating C/C++ applications.

GPU↗

NASA Electronic Parts and Packaging (NEPP) Program: Resources for SmallSats on EEE Parts

From the outside looking in, the NEPP program supports NASA's traditional approach to providing electrical, electronic, and electromechanical (EEE) assurance for space missions. Standards (military and commercial) for EEE parts are based on risk averse methodologies, drive higher costs and schedules, and, in general, provide devices that significantly lag behind commercial devices in performance aspects (speed, power efficiency, etc...). This is NOT the model most small missions realistically can use. However, when you look behind the curtain, NEPP has been considering the risk trade space for small missions for over five years and has consistently provided resources that the small mission regime would find useful. In this paper, we provide a brief overview of these resources as well as NEPP's current research/development efforts that are relevant. While we'll primarily discuss radiation assurance related issues such as data availability and usage, assurances processes for not only the radiation effects side, but also the EEE parts reliability will be touched upon.

Electrical↗

NASA Electronic Parts and Packaging (NEPP) Program - Resources for SmallSats on EEE Parts

From the outside looking in, the NEPP program supports NASA's traditional approach to providing electrical, electronic, and electromechanical (EEE) assurance for space missions. Standards (military and commercial) for EEE parts are based on risk averse methodologies, drive higher costs and schedules, and, in general, provide devices that significantly lag behind commercial devices in performance aspects (speed, power efficiency, etc...). This is NOT the model most small missions realistically can use. However, when you look behind the curtain, NEPP has been considering the risk trade space for small missions for over five years and has consistently provided resources that the small mission regime would find useful. In this paper, we provide a brief overview of these resources as well as NEPP's current research/development efforts that are relevant. While we'll primarily discuss radiation assurance related issues such as data availability and usage, assurances processes for not only the radiation effects side, but also the EEE parts reliability will be touched upon.

Parts assurance↗

Don't Forget About... (Factoring in Everything for Successful Mars Exploration): In Situ Resource Utilization

Using In Situ Resources means reduced transportation requirements from Earth and a larger source of materials than might otherwise be available. Of the many in situ resources available on Mars, perhaps the most valuable is water. One facet of NASA's current Mars Exploration Program is a search for the locations and quantities of water in various forms: Subsurface liquid water aquafers; Surface and subsurface water ice and icy soils - Lineated Valley Fill (LVF), Lobate Debris Aprons (LDAs), Concentric Crater Fill (CCF); Hydrated minerals - Chlorides, Phyllosilicates, Sulfates, etc.; "Average regolith." Access to massive quantities of water could change surface mission concepts of operation and drive site selection. Availability of massive quantities of water could enable or change current assumptions for: Propellant manufacturing; Radiation protection;- "Relaxed" requirements for a closed loop ECLSS (Environmental Control and Life Support System); Crop growth; Improved crew amenities, such as more frequent showers and laundry.

ISRU↗

Overview of the Resource Prospector (RP) Mission

This presentation describes the motivation, development, and key elements of the Resource Prospector lunar rover mission concept. This presentation is a modified version of Introducing the Resource Prospector (RP) Mission, which was presented by Dan Andrews at AIAA Space 2014.

Moon↗

In-Space Propulsion Engine Architecture Based on Sublimation of Planetary Resources: From Exploration Robots to NEO Mitigation

This project, sponsored by the NASA Innovative Advanced Concepts examines how the systematic use of space resources such as frozen volatiles can create a new paradigm in surface power generation for deep space missions. The ubiquitous presence of ices of water, carbon dioxide and other compounds throughout the Solar System under conditions favorable for their sublimation will enable novel in-space propulsion and actuation concepts to become a reality and to address one of NASA's Grand Challenges of "All Access Mobility." Accessing such a resource in the far corners of our interplanetary neighborhood let us conceive exploration missions capable of refueling in the Jovian and Saturnian systems to achieve new goals or reach new destinations. The concept also has potential to apply in-situ propulsion to a comet or an asteroid to deflectits orbit slightly to avoid a future encounter with Earth.

Compounds↗

NASA's Fire Information for Resource Management System (FIRMS): Near Real-Time Global Fire Monitoring Using Data from MODIS and VIIRS

NASA's Fire Information for Resource Management System (FIRMS) provides near-real time active fire / hotspot products from MODIS and VIIRS to users in over 160 countries. The goal of FIRMS is to meet the needs of natural resource and protected area managers that face considerable challenges in obtaining timely satellite-derived information on fires burning within and around their management area. FIRMS has been reliably providing active fire / hotspot data in easy to use formats since its inception in 2006. Fire information is provided through a web map interface, email alerts, a web mapping service, and a range of downloadable files (SHP, CSV, KML and JSON). FIRMS data are used directly by end users and by brokers who take the data and add value to it before re-distributing it.FIRMS was initially developed by the University of Maryland in 2006; it was funded by the United Nations FAO and NASA's Applied sciences program under a NASA ROSES call. In 2012 FIRMS became integrated in to NASA's Land Atmosphere Near real-time Capability for EOS (LANCE); a virtual system that leverages NASAs existing science processing capabilities to deliver NRT data from ten instruments within 3 hours of satellite overpass. This presentation will describe the FIRMS system, provide an overview of the system, briefly describe some of the known applications and describe plans to further integrate the data in to NASA's Global Imagery Browse Services (GIBS) public mapping services and Worldview website.

active fire/hotspots↗

Mars Small-Spacecraft Human Exploration Resource Prospector with Aero-braking (SHERPA): Demonstrating an End-to-End Mission to Phobos Distant Retrograde Orbit

This paper summarizes an end-to-end mission design concept exploring the feasibility of using small satellites together with aero-capture technology to achieve Mars orbit insertion, and subsequent injection into a Phobos-stabilized (or distant retrograde) orbit. The science and mission objectives are to carry out a survey of the mineralogy and morphology of Phobos, to answer basic questions concerning its origin and formation, to test the cohesiveness of Phobos regolith, and to search for potential landing sites for future human or robotic spacecraft. The Mars Small-Spacecraft Human Exploration Resource Prospector with Aero-braking (SHERPA) spacecraft is based on a combination flight-tested prototype vehicle and instruments, and first principle sizing of consumables. The resulting system is fitted with an inflatable aerodynamic decelerator to effect aero-capture into a Mars elliptical orbit, on its way to achieving Phobos orbit. A computational fluid dynamics tool is used to analyze the flow-field and identify potential hot spots during aerodynamic flight. This work advocates for the use of small satellites to test out technologies and operational concepts used in sustained human exploration of Mars, and to carry out scientific exploration of the Mars system. Consistent with a systems engineering approach, this work combines elements of the NASA Human Exploration and Operations Mission Directorate, the Space Technology Mission Directorate, and the Science Mission Directorate, and proposes a scenario for science acquisition, technology verification, trajectory validation, and in-situ resource exploration. We believe these type of missions are essential forerunners to human crewed missions to Mars.

Mission Design↗

Gila Water Resources III - Modeling the Impacts of Post-fire Restoration Methods on Vegetation Recovery in the Gila National Forest

In recent years, wildfires in New Mexico’s Gila National Forest have become increasingly common and more severe. Wildfires can have powerful impacts on hydrology and soil stability, including erosion, flooding, and debris-flows that threaten lives and infrastructure downstream. Vegetation restoration treatments like seeding and mulching can mitigate these effects and facilitate ecosystem recovery. Understanding the effectiveness of various restoration methods is vital to planning a cost-effective and successful post-fire recovery strategy. The immediate response to a fire on US Forest Service land is coordinated by a Burned Area Emergency Response (BAER) team, a group responsible for mitigating immediate post-fire risks to human life, property, and critical natural and cultural resources. This study created a proof-of-concept methodology for a decision-support tool designed to help BAER teams identify the restoration treatments most likely to succeed in a given burned area. Leveraging random forest regression, Google Earth Engine, and Landsat 7 and 8 Earth observations, this study modeled vegetation recovery after the 2013 Silver Fire for seeded areas, seeded/mulched areas, and untreated areas. Treatment type and initial burn severity were the largest drivers of vegetation recovery across the landscape. Seeded/mulched areas showed higher recovery levels than untreated areas three months post-fire, but by four years post-fire, treated and untreated areas displayed similar recovery levels. To produce a robust predictive tool for the Gila National Forest, the model should be trained on many more fires and incorporate post-fire weather conditions into the process. Such a model will help partners ensure efficient resource use and plan effective post-fire restoration strategies.

DEVELOP Project Summary↗

Central Valley Water Resources II: Groundwater Sustainability Management Support in the California Central Valley using GRACE and InSAR Datasets

California’s Central Valley is one of the most productive agricultural regions in the United States, producing a fourth of the nation’s food supply. The water demand in this region is heavily dependent on groundwater resources, resulting in over pumping of aquifers at unsustainable rates during recent periods of severe drought. Over the past century, Central Valley aquifers have experienced a significant decline in groundwater levels, resulting in land subsidence and irreversible loss in groundwater storage. In 2014, the state enacted the Sustainable Groundwater Management Act, requiring high and medium priority subbasins to suspend overdraft and achieve sustainable levels of pumping and recharge by 2042.The California Department of Water Resources (DWR) oversees subbasin groundwater management; however, monitoring remains challenging due to sparse and inconsistent in situ data. To assist the DWR, this project developed a user-friendly executable application and an interactive visualization tool to quantify groundwater storage and land subsidence trends using remotely sensed and in situ data. The team utilized NASA’s Gravity Recovery and Climate Experiment (GRACE), GRACE Follow-On (GRACE-FO), Sentinel-1 C-band Synthetic Aperture Radar (C-SAR) interferograms, and Advanced Land Observing Satellite 2 (ALOS-2) Phased Array L-band Synthetic Aperture Radar 2 (PALSAR-2) interferograms in conjunction with well and GPS measurements to analyze groundwater and subsidence trends. GRACE and well data returns produced a strong Pearson correlation of .84, while Sentinel-1 and GPS data returns produced a Pearson correlation of .41 over the entire Central Valley. These findings suggest remotely sensed GRACE and interferometric SAR data can be used in the absence of in situ data.

DEVELOP Project Summary↗

Resource Scheduling for a Network of Communications Antennas

This paper describes tha Demand Access Network Scheduler (DANS) system for automatically scheduling and rescheduling resources for a network of communication antennas. DANS accepts a baseline schedule and supports rescheduling of antenna and subsystem resources to satisfy tracking goals in the event of changing track requests, equipment outages, and inclement weather.

Deep↗

Enabling Limited Resource-Bounded Disjunction in Scheduling

We describe three approaches to enabling a severely computationallylimited embedded scheduler to consider a smallnumber of alternative activities based on resource availability.We consider the case where the scheduler is so computationallylimited that it cannot backtrack search. The first twoapproaches precompile resource checks (called guards) thatonly enable selection of a preferred alternative activity if sufficientresources are estimated to be available to schedule theremaining activities. The third approach mimics backtrackingby invoking the scheduler multiple times with the alternativeactivities. We present an evaluation of these techniques onMars mission scenarios (called sol types) from NASA’s nextplanetary rover where these techniques are being evaluatedfor inclusion in an onboard scheduler.

Vaquero, Tiago↗

Large Vehicle Lunar Landing Surface Interaction and In-Situ Resource Based Risk Mitigation: Landing & Launch Pads

A key capability required for the exploration of planetary bodies is the ability to land on the surface. Previous work performed by NASA and other institutions has primarily focused on landing small spacecraft on planetary surfaces and the associated small-to-medium thrusters required for the soft landing. In the case of human exploration—particularly the establishment of long duration exploration and habitation outposts—the ability to land large landers, such as the SpaceX Starship, is necessary. These larger landing systems require the use of more powerful engines, with higher engine exhaust temperatures and higher landing loads. Understanding the excavation of material by the engines, as well as the potential for the landing legs to sink into the subsurface, is key in ensuring reliable and safe landings. A further improvement in landing reliability can be achieved by constructing landing / launch pads, especially with in-situ resources. Some material excavation by the plume is inevitable, leaving at least a portion of the surface scoured and uneven under the lander and ejecting regolith particles and rocks at very high velocities. One possible solution would be to robotically build landing / launch pads (ideally autonomously) at the destination using in-situ materials. In this case, the first one or few landers will need to land on unimproved surfaces at higher risk; however, they would bring the required equipment to build the landing pads with mostly local resources, thus increasing the reliability of safe landing for subsequent larger landers. A number of methods to build in-situ landing and launch pads have already been developed. These methods include no or some addition of required binder additives to the local regolith material, different processing approaches and result in varying landing pad strengths. A sub-scale rocket engine plume, was used to simulate some of the conditions of a landing on the Moon to assess the effectiveness of various materials for an in-situ built landing pad, The GO2/GCH4 rocket engine fired on 1m2 area coupons of representative pad materials. The results will allow continued development towards materials that satisfy the landing pad properties required for the effective risk reduction and increased reliability for landing people and equipment on the lunar surface. This work contained two parts: (1) computer modeling of a large rocket engine plume interacting with regolith on the Moon, using the Granular Gas Flow Solver (GGFS) provided by CFD Research Corporation as well as other computational fluid dynamics codes (CFD) such as Loci/CHEM. (2) Developing landing/launch pad materials that could be used for in-situ construction on the lunar surface in the future, to mitigate the calculated effects of a large vehicle rocket engine landing and launching on the Moon. The resulting computed values of plume impingement surface temperature, stagnation pressure, gas velocity, shear stress and heat flux were then matched as closely as possible in the Earth’s atmosphere in a sub-scale rocket engine GO2/CH4 test which was provided by Masten Space Systems in Mojave, California. The rocket engine was mounted on a test stand with vertical translation capabilities so that the landing operations of a lander could be simulated (Figure 1).The pad materials test coupons were placed at the surface of a large bin containing simulated lunar basalt regolith and subjected to a test firing as shown in Figure 2. The results of this testing will be presented with related findings, analysis and discussion.

Plume Surface Interaction↗

In-Space Inspection Needs: Opportunities for advanced NDE tools such as x-ray CT for additively manufactured parts, in-situ resource utilization, geological applications, and more

It is now 50 years since the first human presence on the surface of the Moon and as we strive to return with women and men in the next few years, we embrace new technical challenges, goals, and innovative solutions to address 21st century objectives. These new ambitions carry fresh challenges and risks, with the field of NDE playing an increasingly more relevant role towards meeting these essential goals. In recent years, more advanced NDE tools have triggered a rapid expansion of applications for the space industry. In particular, x-ray Computed Tomography (CT) has proven to be a trusted and powerful asset for spaceflight hardware inspection, as well as applied geotechnical analysis for natural materials (e.g., rocks, soils) for NASA and across industry. However, such methods have yet to be extended to “deep space” applications such as those that are now part of the US National Space Policy Directive (SPD-1) and the accelerated push to return humans to the Moon (i.e., Artemis). For this reason, advancing these powerful Earth-based laboratory methods via new technologies, integrated computational solutions, and creative engineering approaches is directly aligned with national space policies, as well as with multiple NASA Strategic Plan priorities. The use of x-ray CT at scales as fine as a few microns or smaller can identify spacecraft part failure modes relevant to quality assurance for flight hardware and AM parts such as those recently developed for ISS. This technology could also identify valuable metallic phases within geological materials (i.e., rocks or drill cores), enabling resource-relevant triage of samples for In-Situ Resource Utilization (ISRU) and high science value sample return to Earth laboratories. There is also significant application for 3D imaging tools for medical use such as inspecting protective gear as well as bone density degradation studies which are critical in establishing a sustained presence in space. Timing for development of these tools for space use is advantageous as we prepare for new opportunities in the next few years and recognize recent commercial technology advancements which make it feasible. Moreover, as NASA strives to take full advantage of developments in AM technologies, including In-Space Manufacturing (ISM), it is widely recognized that NDE tools such as CT will play an essential role in acceptance of these parts for widespread use. New in-space 3D inspection tools with complimentary technology such as AI-based automated feature recognition (accelerated by machine learning), rapid compositional analysis, and advanced sample manipulation, would be a game-changing step toward a new class of crew-based laboratory sensors once human outposts on the Moon are established.

In-Space Non-Destructive Evaluation↗

Improving Computational Efficiency of Prognostics Algorithms in Resource-Constrained Settings

In engineering and aerospace applications, it is vital to operational success to have insight into the expected performance and health of physical systems. The field of prognostics and health management provides quantitative methods for monitoring, predicting, and managing system health. Prognostics algorithms can be employed to assess the current state of a system, propagate the system throughout time, and predict potential anomalies or failures that may occur. While they can provide accurate prediction results, effective prognostics algorithms can be challenging to use in resource-constrained settings due to computational limitations and high computational latency, leading to obsolete predictions. Thus, computationally efficient and accurate algorithms are necessary for future remaining useful life predictions. In this work, we implement new algorithmic approaches for prediction, quantitatively compare them via a battery degradation use-case, and provide recommendations of potential improvements to a prognostics framework. One approach to prediction is through sampling, whereby the current state of a physical system is sampled many times and each sample is propagated forward until failure is reached, resulting in a distribution of failure values. To improve the efficiency of this process, we implemented five new algorithmic approaches to prediction, including three distinct sampling methods (standard Monte Carlo, Quasi-Monte Carlo, and Latin Hypercube Sampling), a variable time step algorithm, and a variable sample size algorithm. To compare the algorithms, we employ a variety of metrics designed specifically to analyze both computational efficiency and model accuracy. Our metrics include accuracy to compare the average predicted value to ground truth, mean absolute deviation to illustrate dispersion, specific percentile error to describe accuracy within a user-defined risk tolerance, and code run-time. To quantitatively analyze our results, we employ a use-case of degradation of a Lithium-ion battery. We use an electrochemistry-based model to describe the current health state of the battery, and implement our prediction algorithms to propagate forward in time until end-of-discharge (EOD) is reached. Notably, through this work it was found that none of our sampling approaches had a significant impact on computational efficiency or model accuracy in predicting EOD of the battery. We find that while the sampling methods are unique, the distributions they generate are similar, ultimately producing final predictions that are nearly identical. In exploring the effect of the time step within the prediction algorithm, we found that prediction accuracy was highly dependent on the time step used, and that implementing a variable time step within a particular prediction may provide an increase in computational efficiency while also maintaining prediction accuracy. Finally, implementing a variable sample size also affected prediction, and our results show that tuning both the magnitude and timing of the sample size adjustment can result in improved computation speed and maintained prediction accuracy. Taken together, our findings highlight the challenge of performing prognostics in resource-constrained settings, and illustrate the potential of developing new prediction algorithms to improve computational efficiency.

prognostics↗

Large Vehicle Lunar Landing Surface Interaction and In-Situ Resource Based Risk Mitigation: Landing & Launch Pads

A key capability required for the exploration of planetary bodies is the ability to land on the surface. Previous work performed by NASA and other institutions has primarily focused on landing small spacecraft on planetary surfaces and the associated small-to-medium thrusters required for the soft landing. In the case of human exploration—particularly the establishment of long duration exploration and habitation outposts—the ability to land large landers, such as the SpaceX Starship, is necessary. These larger landing systems require the use of more powerful engines, with higher engine exhaust temperatures and higher landing loads. Understanding the excavation of material by the engines, as well as the potential for the landing legs to sink into the subsurface, is key in ensuring reliable and safe landings. A further improvement in landing reliability can be achieved by constructing landing / launch pads, especially with in-situ resources. Some material excavation by the plume is inevitable, leaving at least a portion of the surface scoured and uneven under the lander and ejecting regolith particles and rocks at very high velocities. One possible solution would be to robotically build landing / launch pads (ideally autonomously) at the destination using in-situ materials. In this case, the first one or few landers will need to land on unimproved surfaces at higher risk; however, they would bring the required equipment to build the landing pads with mostly local resources, thus increasing the reliability of safe landing for subsequent larger landers. A number of methods to build in-situ landing and launch pads have already been developed. These methods include no, or some, addition of required binder additives to the local regolith material, different processing approaches and result in varying landing pad strengths. A sub-scale rocket engine plume, was used to simulate some of the conditions of a landing on the Moon to assess the effectiveness of various materials for an in-situ built landing pad, The GO2/GCH4rocket engine fired on a 1m2area coupons of representative pad materials. The results will allow continued development towards materials that satisfy the landing pad properties required for the effective risk reduction and increased reliability for landing people and equipment on the lunar surface. This work contained two parts: (1) computer modeling of a large rocket engine plume interacting with regolith on the Moon, using the Granular Gas Flow Solver (GGFS) provided by CFD Research Corporation as well as other computational fluid dynamics codes (CFD) such as Loci/CHEM. (2) Developing landing/launch pad materials that could be used for in-situ construction on the lunar surface in the future, to mitigate the calculated effects of a large vehicle rocket engine landing and launching on the Moon.

Lunar↗

Improving Computational Efficiency of Prognostics Algorithms in Resource-Constrained Settings

The field of prognostics and health management provides quantitative methods for monitoring and predicting the health of physical systems. Prognostics algorithms are useful in that they can be employed to assess the current state of a system, propagate the system state throughout time, and predict potential anomalies or failures that may occur. However, effective prognosis can be challenging to achieve in resource-constrained settings due to computational limitations and high computational latency, leading to obsolete predictions. Thus, computationally efficient and accurate algorithms are necessary for some prognostics applications. In this work, we implement three new algorithmic approaches to prediction (sampling methods, variable prediction time step, variable prediction sample size) with the goal of improving computational efficiency while minimizing decrease in model accuracy. To quantitatively analyze our results, we examine a use-case of degradation of a Lithium-ion battery. Notably, through this work it was found that none of the sampling approaches had a significant impact on computational efficiency or model accuracy in predicting EOD of the battery. However, our results show that prediction accuracy is highly dependent on the time step used, and that an appropriate time step can optimize both model accuracy and simulation efficiency. Finally, implementing a variable sample size also affected prediction, and our results show that tuning both the magnitude and timing of the sample size adjustment in an application-specific manner may prove useful in some applications. Taken together, our findings highlight the challenge of performing prognostics in resource-constrained settings, and illustrate the potential of developing new prediction algorithms to improve computational efficiency of prognosis.

Prognostics↗

Enhancement of a global lake and reservoir database to aid climate studies and resource monitoring utilizing satellite radar altimetry

Here, we describe the expansion and enhancement of a large (surface area ≥100 sq. km) lake and reservoir database (1.GREALD). These efforts have also resulted in the spin-off of two additional databases, one containing lakes and reservoirs (2.GREALD, area 10–99 sq. km), and the other containing ephemeral lakes (3.GELD, area ≥100 sq. km). These databases are unique sources for projects that utilize satellite radar altimeter data to monitor surface water levels. While 1.GREALD aims to be a complete catalog, 2.GREALD focuses on reservoirs in response to applied sciences programs that monitor water and energy resources. The creation of 3.GELD has climate change objectives as well as water resources and ecosystem conservation applications. The recording of information pertaining to the potential overpasses (waterbody crossings) of the current and archive satellite altimeters is a primary objective as is the need to highlight any form of controlled water level variation. The permanent water databases now contain 6282 entries, half experience some form of anthropogenic influence and ∼430 have been identified as potential climatically sensitive terminal lakes. The revised integral surface area distribution is a power law with exponent −1.016. Statistics reveal that with altimetric repeat visit times of 10-day to monthly, at least 80% of the permanent water bodies (≥10 sq. km) have been overflown at some period since the 1990s. Current information on water use and reservoir formation date show that the primary use of the reservoir class is hydroelectric power, and that China, Brazil, India, Turkey, and Vietnam dominate the dam building in recent decades.

Charon M. Birkett↗